I admit, I didn't think that that was legal. But anyway, the fix is quite trivial and has no affect upon performance:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

my %sequences;

local $/ = '>';
(undef) = scalar <DATA>; ## Discard first delimiter

local $/ = "\n>";

while( my $record = <DATA> ) {
    my @lines = split "\n", $record;
    pop @lines if $lines[-1] eq '>';
    my $id = shift @lines;
    $sequences{ $id } = join'', @lines;
}
pp \%sequences;

__DATA__
>uc002yje.1 > chr21:13973492-13974491
cccctgccccaccgcaccctggattactgcacgccaagaccctcacctga
acgcgccctacactctggcatgggggaacccggccccgcagagccctgga
CTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG
>uc002yje.2 > chr21:13974492-13975432
cccctgccccaccgcaccctggattactgcacgccaagaccctcacctga
acgcgccctacactctggcatgggggaaaaaacccggccccgcagagccctgga
CTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG
>uc002yje.3 > chr21:13975431-13976330
cccctgccccaccgcaccctggattactgcacgccaagaccctcacctga
acgcgccctacactctggcatgggggaacccggccccgcagagggccctgga
CTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG
[download]

Produces:

C:\test>fasta
{
  "uc002yje.1 > chr21:13973492-13974491" => "cccctgccccaccgcaccctggatt
+actgcacgccaagaccctcacctgaacgcgccctacactctggcatgggggaacccggccccgcagagc
+cctggaCTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG",
  "uc002yje.2 > chr21:13974492-13975432" => "cccctgccccaccgcaccctggatt
+actgcacgccaagaccctcacctgaacgcgccctacactctggcatgggggaaaaaacccggccccgca
+gagccctggaCTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG",
  "uc002yje.3 > chr21:13975431-13976330" => "cccctgccccaccgcaccctggatt
+actgcacgccaagaccctcacctgaacgcgccctacactctggcatgggggaacccggccccgcagagg
+gccctggaCTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG",
}
[download]